Functional Analysis and Applications Seminar 

07/03/2003, 14:00 — 15:00 — Room P3.10, Mathematics Building
Ana Moura Santos, Instituto Superior Técnico

An Operator Approach for an Oblique Derivative Boundary-Transmission Problem

We consider a boundary-transmission problem for the Helmholtz equation in a Bessel potential space setting. The boundary is a strip of infinite extent and certain boundary conditions are assumed on it in the form of oblique derivatives. The problem has an interpretation within the context of diffraction theory and we discuss the relevance of oblique derivatives boundary conditions. Operator theoretical methods are used to deal with the problem and, consequently, several convolution type operators are constructed and "associated" to the problem. We also compare these results with the previous construction of operators in the half-plane case. At the end, the well-posedness of the problem is shown for orders of the Bessel potential space near to that of the finite energy norm.